Proceedings of the 2000 IEEE International Conference on Control Applications WM3-5 2~20 Anchorage, Alaska, USA September 25-27,2000 Control System Design for Rotorcraft-based Unmanned Aerial Vehicles using Time-domain System Identification David Hyunchul Shim*, Hyoun Jin Kim*, Shankar Sastry** 'Graduate Students, Department of Mechanical Engineering, University of California at Berkeley "Professor, Department of Electrical Engineering and Computer Science, University of California at Berkeley ( hcshimjin,sastry ] @robotics.eecs.berkeley.edu ABSTRACT research, there are more limitations on accessing test facilities and resources. Hence, it has been often attempted to borrow full size This paper introduces the development of flight control system for helicopter models[ 11 as the template for small-size RUAV rotorcraft-based unmanned aerial vehicle(RUAV). In this research, dynamics, assuming the dynamics of full-size and RUAV are the linear time-invariant model valid for hover is sought. The similar. Unfortunately, this is rather hard to be justified due to the system response data is acquired in carefully devised experiment servorotor mechanism found in almost all of small size procedure and then a linear time-invariant system model is helicopters. The servorotor, or Bell-Hiller Stabilizer system, has a obtained using time-domain analysis method. The acquired model strong damping effect on the rotor dynamics and significantly is used to design feedback controller consisting of inner-loop delays the overall rotor response. In some other cases, it is attitude feedback control, mid-loop velocity feedback control and attempted to design the flight controllers of simple structure by the outer-loop position control. The proposed controller is trial and error during the actual flight. This alternative approach implemented on digital onboard computer and tested in a Berkeley would require only the basic understanding of the plant, but the RUAV and shows outstanding hovering performance. resulting controller by this process is not likely to be the optimal tuning and it is also a very dangerous practice risking damages to 1. Introduction test pilot crews and the costly UAV system. BErkeley AeRobot (BEAR) project aims to organize multiple Therefore, in this paper, we adopt a systematic way to find a number of autonomous agents into integrated and intelligent dynamics model using time-domain system identification method. systems with reduced cognition and control complexity, fault- Once the models are determined, a multi-loop SISO control tolerance, adaptivity to changes in task and environment, structure is designed and implemented on Berkeley RUAVs. The modularity and scalabiIity to perform complex missions experimental setups and the actual flight test results using the efficiently. In this hierarchical structure, UAVs play an important proposed controllers are shown and the results are discussed. role as the mobile aerial units to perform given tasks ordered by ground-based command station via wireless communication 2, System Identification network. Rotorcraft airframe suits our application particularly well due to their versatile maneuverability such as vertical take- It is well known that a helicopter is a very difficult system for off/landing, hovering, sideslip, pirouette, and so on. identification due to its unstable, highly nonlinear, time-varying, and MIMO characteristics. The model also varies significantly During the last decade, significant progresses are made on the depending on the flight mode, hovering or forward flight for development for small-size RUAVs[2,3,4,5]. One of the strongest example, and the measurement is prone to be contaminated by thrusts of this progress was the advent of powerful but small mechanical vibrations. Therefore, we should first decide which microcomputers and navigation sensors. The computing power of mode to identify. In this research, linear time-invariant model is ordinary PC CPU has become sufficient to process vehicle-level chosen to capture the helicopter dynamics in hover. The order of real-time discrete-time control as well as high-level trajectory the model should be chosen depending on the bandwidth of planning and decision making. Strap-down inertial navigation interest. In this research, a model valid for near-hover condition is system (INS) units consisting of micromachined inertial sensors to be obtained for the design of hovering and low-velocity are now available at surprisingly smaller size and lower cost. maneuver. Moreover, the accuracy of INS is remarkably improved using global positioning system (GPS) as the correctional positioning A 6-degrees-of-freedom linear rigid body helicopter model sensor. Advances of the supporting electronics such as compact augmented with first-order approximation of servorotor dynamics wireless communication devices and high capacity batteries also is given by a differential equation contribute to the construction of powerful RUAV less than 10kg. X = AX+Bu (1) The acquisition of high fidelity system model of target UAV is a where crucial step towards the successful design of high-performance flight control system. In general, however, it is a challenging x = [U v p q cp 0 a,, b,, w r rfiIT (2) - process to identify RUAV dynamics due to its multi-input multi- (3) output (MIMO) characteristics, nonlinearity, severe noise and disturbance, and wide flight envelop. Moreover, in RUAV 0-7803-6562-3/00$10.0002000IEEE 808 U, v, w: body-coordinate velocity stabilizer bar. The equations also include the input coupling terms, @, 0, Y : roll, pitch, yaw angle, respectively which are not small as shown in Eq. (4). The angular rate p, q, r : roll, pitch, yaw rate, respectively dynamics is coupled with blade flapping angles (a,,, b,, ) and body velocities (U, Translational body velocity and v mainly a,, , b,, : flapping angle v). U are affected by the sum of the tilt angle and the flapping angles in rfi : feedback gyro system state . each roll and pitch direction. One candidate model of eleventh order takes the form of Eq. (4) as The heave dynamics is approximated by first order quasi-static suggested by Mettler et a1 [2]. One distinction of this model is the model. This model yields linear, low-order approximation of the explicit account for the servorotor, which modifies the helicopter highly nonlinear high order heave dynamics. For higher bandwidth dynamics significantly .-Commonly used servorotor for small-size controllers, the third or fourth order of model containing inflow RUAV is Bell-Hiller stabilizer system, which has a pair of paddle- and flapping dynamics should be used [8]. Yaw dynamics is also shaped blades that are connected to the main blades by a series of stable and modeled as first order system with reasonable fidelity. mechanical linkages. The most important role of servorotor is to One special feature of yaw dynamics is the built-in feedback slow down the roll and pitch response so that human pilot on the action of yaw rate in the loop, which is provided by the ground can control the helicopter with remote controller. The commercially available rate gyro amplifier. Even though the dynamics can be described as coupled first order model as uncompensated yaw dynamics is stable, the variation of the anti- following[2]: torque of the main rotor continually perturbs the heading of the helicopter. The yaw rate feedback counteracts the torque by compensating the tail rotor collective pitch and is chosen to remain in the system for manual flights. The gyro system model is also suggested by Mettler 121 and it is very effective to capture the dynamics with high accuracy, as shown in Figure 1. One deficiency of the model (4) is the absence of the cross-coupling from yaw to sideslip and roll. It can be additionally parametrized in the model, but it turned out during the numerical process that 2, can be interpreted as the time constant of the servorotor the additional parameters are cumbersome to find because they response to the swash plate tilt angles. The body angular rate p and appear as a product of parameters and the numerical process q appear as feedback terms because of the gyroscopic effect of the becomes singular. -0.0629 0 0 0 0 -g -g 0 0 0 0 0 0.0305 0 OgO 0 g 0 0 0 0.2978 -0.7061 0 000 40.361 237.42 0 0 0 1.3057 - 1.2 199 0 000 220.18 -11.438 0 0 0 0 0 1 000 0 0 0 0 0 A= 0 0 0 100 0 0 0 0 0 (4) 0 0 0 -1 0 0 -4.3459 1.4487 0 0 0 0 -1 000 -1.5915 -4.3459 0 0 0 1: 0 0 000 -3.0523 -15.063 -1.3453 0.2222 0 0 -0.0178 000 0 0 1.1860 -2.9986 -22.126 0 0 000 0 0 0 3.1541 -9.5035 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Table 1. Eigenvalues of the identified helicopter system 0 0 0 0 I Mode I Value B= 0 0 0 0 Phugoid 1 -0.3184k0.5 157j 0.5259 2.1922 0 0 Phugoid 2 0.0087*0.5675j Roll -2.4425k 15.6953j 2.2333 -0.0917 0 0 Pitch -2.1723k14.9316i 0 10.6446 0 0 4.491 1 -1 03.335 Heave -1.3134 0 0 0 - 809 Since the model is treated as a linear model, the nonlinearity of helicopter aerodynamics should not be excited by the excessive amount of control action. Hence, the appropriate design of control input signals for flight test is extremely important for the identification of target flight dynamics. A number of experimental flights have been made to collect the flight data and the pilot input at 50Hz sampling rate. The control input consists of the combination of frequency-sweeping and random signals in longitudinal, lateral, yaw and heave channels in turn.